Test 2

Please do all your work on this test. Use
a PENCIL; do not use a pen. Write in complete sentences
and express yourself clearly. Be precise, yet concise.

Use the extra sheets at the end of the test if you need extra
space. Be sure to label your work on the extra sheets with the
problem number it goes with.

Good luck! Do a good job!

General Motors divisions (Chevrolet, Buick, Oldsmobile, etc.)
manufactured approximately 35% of all automobiles owned in Middle
Tennessee. One morning, while sitting at a red light, Brady noticed
that the 5 cars around him (1 in front, 3 aside, 1 in back) were
all GM automobiles.

What would it mean for this event to be "statistically
unusual"?

How would you investigate whether this event is, in fact,
statistically unusual?

The histogram and table below show the simulated results
of selecting 10,000 random samples of 1024 people, each sample
taken from a large population of which .40 believe "yes"
on some subject.

What does "0.38" stand for in the column under
"Interval Start"?

What does "50" stand for under in the column under
"Counts"?

We are going to simulate collecting 3000 random samples of
size 1024 people, but from a population of which .60 believes
"yes". Approximately what fraction of those samples
will have between .59 and .61 of the people in them believing
"yes"?

Here is a table similar to one we filled out in an in-class
activity. Use it in answering parts a through e.

Percent
of Yes in Population

Number
of People in a Sample

Number
of Samples Drawn

% of
Sample Percents within 1 Percentage Point of Population %

% of
Sample Percents within 2 Percentage Points of Population %

% of
Sample Percents within 3 Percentage Points of Population %

% of
Sample Percents within 4 Percentage Points of Population %

65%

500

2500

36.7%

64.5%

84.8%

91.5%

32%

500

2000

37.1%

65.8%

83.9%

91.1%

57%

500

6800

36.2%

64.9%

84.2%

91.3

60%

500

5500

36.1%

65.2%

84.3%

91.4%

To how many populations does this table
refer?

The entry in column 5, row 3 is 64.9%. That refers to 64.9%
of what (be specific)?

The entry in column 1, row 4 is 60%. That refers to 60% of
what (be specific)?

All the percents in each of columns 4 through 7 are approximately
the same. What can we conclude from that?

Stan's statistics class was discussing a Gallup poll of 500
TN voters' opinions regarding the creation of a state income
tax. The poll stated, " the survey showed that 36%
of Tennessee voters think a state income tax is necessary to
overcome future budget problems. The poll had a margin of error
of ±4%."

Stan said that the margin of error being 4% means that between
32% and 40% of TN voters believe an income tax is necessary.

Is Stan's interpretation a good one? If so, explain. If not,
what should it be?

The Harris and Gallup companies are well known for conducting
public opinion polls in America. Typically, they make a claim
about what some population believes on a subject and base that
claim on one sample drawn at random from that population.

If statistical claims about populations are typically made
on the basis of collecting a single sample, why have we spent
so much time in class discussing simulations of drawing thousands
of samples?